PPN Parameter Dashboard
Theorem 3.6: the ether’s field equation is the Einstein equation, so all 10 post-Newtonian parameters match GR exactly (Eq 3.186). Despite possessing a preferred rest frame, the ether produces no preferred-frame effects in gravitational experiments — the law is covariant even though the solutions are not.
All 10 PPN Parameters (Theorem 3.6, Eq 3.186)
| Parameter | Ether | GR | Observational bound | Experiment |
|---|---|---|---|---|
| γ | 1 | 1 | |γ−1| < 2.3×10⁻⁵ | Cassini Shapiro delay |
| β | 1 | 1 | |β−1| < 8×10⁻⁵ | Perihelion precession + LLR |
| ξ | 0 | 0 | |ξ| < 10⁻³ | Spin precession |
| α₁ | 0 | 0 | |α₁| < 10⁻⁴ | Orbital polarisation |
| α₂ | 0 | 0 | |α₂| < 10⁻⁷ | Solar spin alignment |
| α₃ | 0 | 0 | |α₃| < 4×10⁻²⁰ | Pulsar spin-down |
| ζ₁ | 0 | 0 | |ζ₁| < 2×10⁻² | Binary pulsar |
| ζ₂ | 0 | 0 | |ζ₂| < 4×10⁻⁵ | Binary acceleration |
| ζ₃ | 0 | 0 | |ζ₃| < 10⁻⁸ | Newton 3rd law |
| ζ₄ | 0 | 0 | — | Linked to other ζ |
Why all zeros? The ether’s field equation is the Einstein equation (Theorem 3.5). By Will’s classification theorem, any metric theory with the Einstein equation has all 10 PPN parameters equal to their GR values. The preferred-frame parameters vanish because the law is covariant — the preferred frame is a property of the state, not the equation.
Classical Tests of Gravity
| Test | Equation | Ether prediction | Observation | Depends on |
|---|---|---|---|---|
| Mercury perihelion precession | Eq 3.184 | 43.00 arcsec/century | 42.98 ± 0.04 arcsec/century | β, γ |
| Solar limb light bending | Eq 3.183 | 1.7517 arcsec | 1.7512 ± 0.0002 arcsec | γ |
| Shapiro time delay (Cassini) | Eq 3.182 | γ = 1 → (1+γ) = 2 | |γ−1| < 2.3×10⁻⁵ | γ |
| Nordtvedt effect (SEP) | 4β − γ − 3 | 0 (exact) | |η| < 5.6×10⁻³ | β, γ |
Momentum Conservation
ζ1 = ζ2 = ζ3 = ζ4 = 0
GW carries momentum; the ether transmits it via §3.7 mechanism
Strong Equivalence
4β − γ − 3 = 0
Gravitational binding energy gravitates identically to all other energy
No Preferred Frame
α1 = α2 = α3 = 0
Despite ether rest frame, field equation is covariant (§3.12.7)
Numerical Verification
Beta Tools are under active development. Equations are verified against the monograph but outputs may be refined. Report an issue